Don't know anything about AMD System Monitor. Try Core Temp RC6. AMD engineering says they will be fixing AMD Overdrive in the next iteration so it reads temps properly.
Core temp is the only temp that counts and as long as it's below the AMD specified max 24/7 temp you're good to go. While none of the software temp applets are accurate below about 40C on AMD FX CPUs and APUs, in the 40C-70C range, AMD engineering advises they are pretty close.
Building a reliable PC involves more than just assembling the parts. You need to be able to configure all of the BIOS settings appropriately. This can be quite involved and frustrating as it can require a lot of trial and error with stress testing. It is however often the only means to get a 100% reliable PC.